Download Ma 322: Biostatistics Homework Assignment 9

Ma 322: Biostatistics
Homework Assignment 9
Prof. Wickerhauser
Due Friday, April 7th, 2017
Read Chapter 15, “ANOVA and Regression,” pages 263–287 of our text.
NOTE: It should be possible to cut and paste the data from this document into a text file, or into an R
variable by use of the scan() function.
1. (a) How many 2 × 2 contingency tables are there with row sums (2, 5) and column sums (3, 4)? (Hint:
Write down all the solutions.)
(b) Assuming that the rows and columns are independent, compute the exact hypergeometric probability of each 2 × 2 contingency table in part a.
2. The following data are frequencies of bats found with and without rabies in two different geographic
areas:
Area
E
W
With rabies
18
11
Without rabies
112
139
(a) Using the Yates-corrected χ2 test at the α = 0.05 significance level, test H0 : the incidence of rabies
is the same in both areas.
(b) Use the Fisher exact test at the 0.05 level to test if the E population bats are more likely to have
rabies than those in the W population.
3. A follow-on study was performed on the same bats data, similar to that of Problem 2 but with the
additional tabulation of gender:
Area
E
W
With
Male
6
9
rabies
Female
12
2
Without rabies
Male Female
49 63
84 55
(a) Test for mutual independence at the α = 0.1 significance level.
(b) Test for partial independence at the α = 0.05 significance level.
1
4. The following fake data mimics a study of amino acids in six imaginary species of millipedes:
Alanine concentration in millipede hæmolymph (mg/100 ml)
Species 1
21.5
19.6
20.9
22.8
Species 2
14.5
17.4
15.0
17.8
Species 3
16.0
20.3
18.5
19.3
Species 4
14.8
15.6
13.5
16.4
Species 5
12.1
11.4
12.7
14.5
Species 6
14.4
14.7
13.8
12.0
(a) Test, at the α = 0.05 significance level, the hypothesis H0 : There is no difference in mean alanine
concentration among the species. Use one-factor ANOVA.
(b) Test, at the α = 0.05 significance level, the hypothesis H0 : There is no difference in mean alanine
concentration between species A and B. Use pairwise t-tests for every pair A, B.
(c) Test, at the α = 0.05 significance level, the hypothesis H0 : There is no difference in mean alanine
concentration between species A and B. Use Tukey’s HSD test for every pair A, B.
5. Test for all factor and interaction effects in the following 3 × 2 fixed-effects analysis of variance with
equal replication:
Response
a1
---------b1
b2
---- ---34.1 35.6
36.9 36.3
33.2 34.7
35.1 35.8
34.8 36.0
to Factors A and B
a2
a3
------------------b1
b2
b1
b2
---- ------- ---38.6 40.3
41.0 42.1
39.1 41.3
41.4 42.7
41.3 42.7
43.0 43.1
41.4 41.9
43.4 44.8
40.7 40.8
42.2 44.5
6. Test for all factor and interaction effects in the following 4 × 3 × 2 fixed-effects analysis of variance,
where ai is the level of factor A, bi is the level of factor B, and ci is the level of factor C.
a1
------------b1
b2
b3
--- --- ---
Response to Factors A, B and C
a2
a3
------------------------b1
b2
b3
b1
b2
b3
--- --- ----- --- ---
a4
------------b1
b2
b3
--- --- ---
4.1
4.3
4.5
3.8
4.6
4.9
4.2
4.5
3.7
3.9
4.1
4.5
4.9
4.6
5.3
5.0
5.2
5.6
5.8
5.4
4.7
4.7
5.0
4.5
5.0
5.4
5.7
5.3
6.1
6.2
6.5
5.7
5.5
5.9
5.6
5.0
3.9
3.3
3.4
3.7
4.4
4.3
4.7
4.1
3.7
3.9
4.0
4.4
4.8
4.5
5.0
4.6
5.6
5.8
5.4
6.1
5.0
5.2
4.6
4.9
4.9
5.5
5.5
5.3
5.9
5.3
5.5
5.7
5.0
5.4
4.7
5.1
6.0
5.7
5.5
5.7
6.0
6.3
5.7
5.9
6.1
5.3
5.5
5.8
4.1
3.9
4.3
4.0
4.9
4.7
4.9
5.3
4.3
4.1
3.8
4.7
c1:
c2:
2